System and method for inside can inspection

ABSTRACT

A system and method for imaging an interior of a substantially cylindrical object are disclosed. In accordance with an embodiment of the present invention, a substantially cylindrical illuminator is positioned above an opening of a substantially cylindrical object to be imaged (e.g., a beverage can) in order to illuminate at least a portion of the interior surface of the object. A truncated conical mirror is positioned within an interior space of the illuminator to reflect an image of at least a portion of the interior surface of the object. A single camera is positioned above the illuminator and mirror to capture a single image of at least the interior surface of the object via light reflected directly from at least a portion of the interior surface of the object to the camera and from the mirror to the camera. The entire interior surface of the object is captured in the single image which may be analyzed for defects.

CROSS-REFERENCE TO RELATED APPLICATIONS/INCORPORATION BY REFERENCE

This U.S. patent application is a division of and claims priority topending U.S. patent application Ser. No. 11/035,415 filed on Jan. 13,2005 which is incorporated herein by reference in its entirety. U.S.patent application Ser. No. 10/849,955, filed on May 19, 2004, isincorporated herein by reference in its entirety.

TECHNICAL FIELD

Certain embodiments of the present invention relate to automated productinspection. More particularly, certain embodiments of the presentinvention relate to a vision system for imaging the interior of beveragecans on a production line with at least a single camera to identifydefects.

BACKGROUND

In the beverage can industry, it is desirable to have a reliable andeconomical system and method for inspecting the interior surfaces ofcertain objects such as beverage cans and containers. Today,manufacturing processes may move, for example, aluminum beverage cansdown a conveyor line at speeds of at least 2000 cans per minute. Duringthe manufacturing of the beverage cans, defects may be formed on theinterior surface of the cans. It is desirable to reject cans with suchdefects. Ideally, the interior surface of the cans should be free ofphysical defects such as puckers and dents. Also, the interior surfaceshould be free of blistered or non-uniform coatings, oil, grease, anddebris. The flanges of the cans should be free of knockdowns as well.Typically, these types of flaws occur during the manufacturing of thecans or due to contamination of the cans after manufacturing but beforefilling with, for example, a beverage.

Machine vision systems are typically used to inspect objects ofmanufacture such as beverage cans and containers. Machine visiontechnology allows an image of at least a portion of the object to besensed and captured. The image may then be processed to determine if anydefects are present. Typically, cameras are used to acquire images ofthe object and a computer or computers are used to process the image.Human vision is very good at analyzing complex objects and scenes but ahuman is not good at performing repeated tasks over a long period oftime without tiring and making mistakes. Machine vision technologyallows for sophisticated image acquisition, processing, and analysis ofcans and containers on a manufacturing line and provides repeatableperformance in real time.

Inspection of cans and containers via machine vision systems presentscertain challenges. For example, if the cans or containers are opaque,the vision system must operate on light reflected from the surfaces ofthe regions to be inspected. Also, the geometry of cans and containerspresents various challenges. For example, a typical metal can has a neckthat extends upward and radially inward to form an open-topped neckhaving a smaller radius than the rest of the can. Such a design makes itharder to illuminate and image the entire interior of the can,especially around the surface of the neck of the can.

The field-of-view of cameras used for imaging are often limited and makeimaging of the entire interior of an object difficult. For example, widelens aperture cameras are often used to detect small, unacceptabledefects in low light conditions. The depth of focus of a wide lenscamera is typically smaller than the height of a beverage can.Therefore, to capture a good image for inspection, the region of theinterior surface being imaged using a single camera is, typically, onlya portion of the can. A typical beverage can, for example, has avertical height that does not easily allow a single camera to generate asingle image which captures the entire interior of the can, includingthe rim, neck, sides, and bottom of the can, with sharp focus.

U.S. Pat. No. 5,699,152 to Fedor et al. describes a system and methodfor inspecting opaque objects, such as metal beverage containers. Thesystem includes a light source for illuminating the interior surface ofthe container, an ellipsoidal first mirror for forming a first image ofan upper interior portion of the container, a first camera for capturingthe first image of the upper interior portion of the container, a planarimage-splitting second mirror for forming a second image of the flangeof the container, a second camera for capturing the second image of theflange, an image combiner for electro-optically combining the first andsecond images, whereby a resultant composite image corresponding tosubstantially the entire upper interior surface of the container can begenerated and analyzed for defects, a third camera located at a separatelocation for viewing directly the lower interior portion of thecontainer and capturing a corresponding third image, and a computermeans for analyzing the resulting images for defects. Such a system isvery complicated, may be difficult to maintain, and can be ratherexpensive.

It is desirable to figure out how to image the entire interior ofbeverage cans and containers, as well as the interiors of substantiallycylindrical objects in general, using at least a single camera thatprovides acceptable image quality to minimize cost, complexity, andmaintainability of such a vision system.

Further limitations and disadvantages of conventional, traditional, andproposed approaches will become apparent to one of skill in the art,through comparison of such systems and methods with the presentinvention as set forth in the remainder of the present application withreference to the drawings.

BRIEF SUMMARY

An embodiment of the present invention comprises a system for imaging aninterior surface of a substantially cylindrical object. The systemincludes a substantially cylindrical illuminator, positionedsubstantially to one side of an opening of the cylindrical object to beimaged, to illuminate at least a portion of the interior surface of thecylindrical object. The system further includes a truncated conicalmirror positioned substantially within the cylindrical illuminator toreflect an image of at least a portion of the interior surface of thecylindrical object. The system also includes a single camera positionedsubstantially to one side of the cylindrical illuminator and conicalmirror to capture a single image of at least the interior surface of thecylindrical object. The single image is formed from at least lightreflected directly from at least a portion of the interior surface ofthe cylindrical object to the camera and from the conical mirror to thecamera.

Another embodiment of the present invention comprises a system forimaging an interior surface of a substantially cylindrical object. Thesystem includes a substantially cylindrical illuminator, positionedsubstantially to one side of an opening of the cylindrical object to beimaged, to illuminate at least a portion of the interior surface of thecylindrical object. The system also includes a single camera positionedsubstantially to one side of the cylindrical illuminator to capture asingle image of at least a portion of the interior surface of thecylindrical object. The single image is formed from at least lightreflected directly from at least a portion of the interior surface ofthe cylindrical object to the camera.

A further embodiment of the present invention comprises an apparatus forilluminating at least a portion of an interior of a substantiallycylindrical object. The apparatus includes an LED (light emitting diode)holder forming a substantially cylindrical surface and a plurality ofLEDs positioned around and held in place by the LED holder forming asubstantially cylindrical arrangement of the plurality of LEDs. An axisof illumination of each LED of the plurality of LEDs pointssubstantially into an interior cylindrical volume circumscribed by theLED holder.

Another embodiment of the present invention comprises a method ofconstructing a system to image an interior surface of a substantiallycylindrical object. The method comprises positioning a substantiallycylindrical illuminator substantially to one side of an opening of asubstantially cylindrical object to be imaged to illuminate at least aportion of an interior surface of the object. The method also includespositioning a truncated conical mirror substantially within an openinterior region of the illuminator to reflect an image of at least aportion of the interior surface of the object. The method furtherincludes positioning a single camera substantially to one side of theilluminator and the mirror to capture a single image of at least theinterior surface of the object via light reflected at least directlyfrom at least a portion of the interior surface of the object to thecamera and from the mirror to the camera. The method also comprisesaligning the central axes of the illuminator, the mirror, and the camerawith a central axis of the object to be imaged and mounting the alignedilluminator, mirror, and camera to fix the alignment.

These and other advantages and novel features of the present invention,as well as details of an illustrated embodiment thereof, will be morefully understood from the following description and drawings.

BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS

FIGS. 1A and 1B illustrate an embodiment of a system for imaging aninterior surface of a substantially cylindrical object, in accordancewith various aspects of the present invention;

FIG. 2 illustrates an embodiment of a substantially cylindricalilluminator used in the system of FIGS. 1A and 1B, in, accordance withvarious aspects of the present invention;

FIG. 3 illustrates an embodiment of a method to construct the system ofFIGS. 1A and 1B to image an interior surface of a substantiallycylindrical object, in accordance with various aspects of the presentinvention;

FIG. 4 illustrates an exemplary embodiment of a single image formed bythe system of FIGS. 1A and 1B, in accordance with various aspects of thepresent invention;

FIG. 5 illustrates an exemplary can imaging geometry, in accordance withan embodiment of the present invention; and

FIG. 6 illustrates an exemplary graph of radial position on a CCDcorresponding to a given distance down a neck of a beverage can, inaccordance with an embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

FIGS. 1A and 1B illustrate an embodiment of a system 100 for imaging aninterior surface of a substantially cylindrical object 110, inaccordance with various aspects of the present invention. The system 100comprises a substantially cylindrical illuminator 120, a truncatedconical mirror 130, a camera 140, and a computer-based platform 150.

The illuminator 120 is positioned to one side of (e.g., above) theobject 110 to be imaged. The function of the illuminator 120 is toilluminate at least a portion of the interior surface of the object 110(e.g., the rim or flange and neck of a beverage can). In accordance withan embodiment of the present invention, the illuminator 120 is centeredabove an open top 115 of a beverage can 110.

A truncated conical mirror 130 is positioned substantially within anopen interior region of the illuminator 120 such that an image of atleast a portion of the interior of the object 110 (e.g., the flange andneck) is reflected onto the mirror 130. The dimensions and positioningof the mirror 130 are such that the mirror 130 allows light from theilluminator 120 to enter the interior of the object 110 through anopening 115 in the object 110.

A single camera 140 is positioned substantially to one side (e.g.,above) the illuminator 120 and mirror 130 such that a single image of atleast the entire interior of the object 110 may be captured by thecamera 140. The central axes of the camera 140, mirror 130, andilluminator 120 are all aligned along the system axis 160 which isaligned with a central axis of the object 110 to be imaged. The lens ofthe camera 140 is directed toward (e.g., downward) the object 110 to beimaged. The camera 140 is positioned such that a field-of-view 145 ofthe camera encompasses the mirror 130 and the object 110 to be imaged.

In accordance with an embodiment of the present invention, the camera140 comprises a digital camera (e.g., a CCD camera) which interfaces tothe computer-based platform 150 via an Ethernet connection 155. An imageis captured digitally by the camera 140 and transferred to thecomputer-based platform 150 via the Ethernet interface 155. Thecomputer-based platform 150 stores and analyzes the transferred digitalimage. As an alternative, the camera 140 comprises an analog camera anda frame grabber is used to capture and digitize an analog image from thecamera 140. The resultant digitized image is then sent to thecomputer-based platform 150 as before. In accordance with a particularalternative embodiment of the present invention, the frame grabber is apart of the computer-based platform 150.

In accordance with an embodiment of the present invention, thecomputer-based platform 150 includes a personal computer (PC) and isused to analyze digital images from the camera 140 for defects of theinterior surface of the object 110 such as, for example, puckers, dents,and knockdowns. Also, blistered or non-uniform coatings, oil, grease,and debris are also detected. The configuration of the system 100, usinga single camera 140, affords a relatively small footprint that allowsthe system 100 to be used in relatively tight spaces.

In FIG. 1B, a relative relationship between the object 110, illuminator120, and mirror 130 is readily apparent. Also, FIG. 1B shows a top viewof the illuminator 120. In accordance with an embodiment of the presentinvention, the illuminator 120 comprises a substantially cylindricallight-emitting-diode (LED) holder 121. The LED holder 121 forms asubstantially cylindrical surface into which a plurality of LEDs 122 maybe mounted. Holes are machined into the holder 121 (two holes for eachLED to be mounted) and the conductive leads of the LEDs 122 are passedthrough the holes in the holder 121 to position the LEDs 122 in theholder 121.

In accordance with an embodiment of the present invention, the LEDs 122are positioned around the LED holder 121 forming four (4) rows of eighty(80) LEDs per row, stacked vertically on top of each other. The four (4)rows are horizontally oriented, each row forming a circle around theinterior of the LED holder 121. The four (4) rows form a substantiallycylindrical arrangement of the plurality of LEDs. For each LED 122, anaxis of illumination (i.e., a line along which light is maximallytransmitted from an LED) points substantially downward and into aninterior cylindrical volume circumscribed by the LED holder 121. TheLEDs 122 emit a spectrum of white light substantially along the axes ofillumination. However, other colored LEDs may be used in accordance withvarious alternative embodiments of the present invention. For example,blue illumination may provide better contrast for certain defects insidea beverage can.

Even though FIGS. 1A and 1B show a vertically aligned orientation of thesystem 100 with the camera pointed downward, other orientations arepossible as well as long as the central axes of the camera, mirror,illuminator, and object to be imaged are all aligned along a singlesystem axis, in accordance with various embodiments of the presentinvention. Also, a protective enclosure 180 (see FIG. 1A) may beprovided as part of the system 100, especially to protect the camera 140and the assembly of the mirror 130 and illuminator 120.

In accordance with an alternate embodiment of the present invention, themirror 130 is eliminated from the system 100. Such a configuration maybe used to image the interior surface of an object where the camera 140has a direct line of sight at the entire interior surface, or where itis not required to image the entire interior surface of the object, forexample.

For example, in accordance with an alternative embodiment of the presentinvention, two separate imaging stations may be provided with eachimaging station having its own camera. The first imaging station is usedto image a lower interior portion of a beverage can using a singlecamera and a cylindrical illuminator, and a second imaging station isused to image an upper interior portion of the beverage can using asingle camera, a cylindrical illuminator, and a truncated conicalmirror. The two imaging stations may be in series on an inspection line.Other configurations are possible as well, using various combinations ofilluminators, mirrors, and single cameras at separate imaging stations.

FIG. 2 illustrates an embodiment of a substantially cylindricalilluminator 120 used in the system 100 of FIGS. 1A and 1B, in accordancewith various aspects of the present invention. Again, the illuminator120 includes a holder 121 and a plurality of LEDs 122 forming asubstantially cylindrical arrangement. A horizontal directionalcomponent of illumination 201 of each LED 122 is pointed such that thehorizontal directional component of illumination 201 does not intersectan imaginary vertical central axis 202 of the interior cylindricalvolume of the illuminator 120.

Also, the horizontal directional component of illumination 201 of eachLED 122 is pointed at a same predetermined horizontal angle 203 (e.g.,4° 30′) with respect to a horizontal directional component ofillumination of an adjacent LED 122 in a same horizontally oriented rowof LEDs 122 as seen in FIG. 2. As a result, the horizontal planeconfiguration of LEDs 122 as shown in FIG. 1B results.

Each LED 122 of the illuminator 120 also has an elevational directionalcomponent of illumination. FIG. 2 shows four (4) rows of LEDs 122 whereeach row corresponds to a different elevational directional component ofillumination, in accordance with an embodiment of the present invention.In a first or top row 210, the LEDs 122 are pointed downward along afirst elevation directional component of illumination 125 of 45° withrespect to horizontal. In a second row 220, the LEDs 122 are pointeddownward along a second elevational directional component ofillumination 126 of 37° with respect to horizontal. In a third row 230,the LEDs 122 are pointed downward along a third elevational directionalcomponent of illumination 127 of 28° with respect to horizontal. In afourth or bottom row 240, the LEDs 122 are pointed downward along afourth elevational directional component of illumination 128 of 18° withrespect to horizontal.

The compound angle formed by the horizontal directional component ofillumination and the elevational directional component of illuminationfor each LED helps to project light an angles to produce a shadow in thecaptured image when a “pucker” defect is present. Such shadows allow foreasier detection of the “pucker” defects by the computer-based platform150.

As can be seen in FIG. 1B, such a configuration of LEDs 122 provideillumination of at least an upper portion of the interior of the object110 to be imaged, including the neck 111 of the object 110 (e.g., theneck of a beverage can) to make good use of the mirror 130. However,light from the illuminator 120 also helps to illuminate the entireinterior of the object 110 due to reflections of the light within theobject 110.

In accordance with an embodiment of the present invention, a flexibleprinted circuit board (not shown) is wrapped around the outside of theLED holder 121. The conductive electrical leads of the LEDs 122 passthrough holes in the LED holder 121 and holes in the flexible printedcircuit board. The conductive electrical leads of the LEDs 122 aresoldered to the back of the flexible printed circuit board. As a result,electrical power may be provided to the LEDs 122 via the flexiblecircuit board and the soldered leads help to hold the LEDs 122 in place.In accordance with an alternative embodiment of the present invention,each row of LEDs may be controlled (i.e., turned on and off) separately.Such control provides flexibility in how the interior of a beverage canis illuminated to optimize the illumination for each particular style ofcan.

Also, in accordance with an embodiment of the present invention, the LEDholder 121 includes a first upper lip 123 and a second lower lip 124(see FIG. 1B) to help protect the LEDs 122 from physical damage oncethey are mounted within the holder 121. In accordance with variousembodiments of the present invention, the LED holder is made of anon-conductive, machineable, environmentally stable material such asplastic (e.g., phenolic).

The exact dimensions and parameters of the substantially cylindricalilluminator 120 and the truncated conical mirror 130 is a function of atleast the type and design of the object 110 to be imaged.

In accordance with an alternate embodiment of the present invention, thesubstantially cylindrical illuminator may not include LEDs at all. Forexample, the illuminator may instead comprise a ring of neon tubing or aring of fluorescent lighting.

FIG. 3 illustrates an embodiment of a method 300 to construct the system100 of FIGS. 1A and 1B to image an interior surface of a substantiallycylindrical object, in accordance with various aspects of the presentinvention. In step 310, a substantially cylindrical illuminator ispositioned to one side of an opening of a substantially cylindricalobject to be imaged in order to illuminate at least a portion of theinterior surface of the object. In step 320, a truncated conical mirroris positioned substantially within an open interior region of theilluminator to reflect an image of at least a portion of the interiorsurface of the object. In step 330, a single camera is positionedsubstantially to one side of the illuminator and mirror to capture asingle image of at least the interior surface of the object via lightreflected at least directly from at least a portion of the interiorsurface of the object to the camera and from the mirror to the camera.In step 340, the central axes of the illuminator, mirror, and camera arealigned with a central axis of the object to be imaged. In step 350, thealigned illuminator, mirror, and camera are mounted to fix thealignment.

The resultant orientation of the system 100 using the method 300 may bevertical, horizontal, left, right, or any other orientation, as long asthe central axes are aligned as described previously. Also, theparameters of the camera 140 and exactly how the camera 140 ispositioned is a function of at least the type and design of the object110 to be imaged.

The method 300 further includes interfacing the single camera 140 to acomputer-based platform 150 for storing and analyzing images. The method300 also includes providing electrical power to the camera 140,computer-based platform 150, and illuminator 120. Electrical power maybe provided by a separate power source 170 (see FIG. 1A) of the system100 such as a power supply or battery. As an alternative, a power supplyin the computer-based platform 150 can provide power for thecomputer-based platform 150, the camera 140, and the illuminator 120, inaccordance with an embodiment of the present invention.

In a typical manufacturing/inspection environment, the system 100 ismounted over a conveyor system line which passes objects (e.g.,open-topped beverage cans) past the system 100 such that the objectspass through the field-of-view 145 of the system 100. The system 100 maybe synchronized to the conveyor system line such that, whenever anobject 110 is entirely within the field-of-view 145 of the system 100,the system 100 captures an image and analyzes the image for defects. Ifan unacceptable defect is found for a particular object 110, the object110 is purged from the conveyor system line. In accordance with anembodiment of the present invention, images are captured and analyzedfast enough such that a conveyor system line running at speeds in excessof 2000 objects per minute may be accommodated by the system 100.

FIG. 4 illustrates an exemplary embodiment of a single image 400 formedby the system 100 of FIGS. 1A and 1B, in accordance with various aspectsof the present invention. The single image 400 is of a typical soda can.The image 400 includes a first part which includes the reflection of therim or flange 410 and the upper portion 420 of the interior surface ofthe soda can from the truncated conical mirror 130 to the camera 140.The first part of the image is spread out by the mirror 130 (i.e., isnot to scale) and images at least the rim and neck of the soda can toabout 25% of the way down the vertical length of the soda can. The image400 also includes a second part which is imaged directly from the sodacan to the camera 140 and includes a reflection of the rim or flange430, the lower portion 440 of the interior surface of the soda can, andthe bottom 450 of the soda can.

The first part of the image 400, which is from the mirror 130, is animage part that corresponds to an opposite side of the soda can. Forexample, referring to FIG. 1B, the image appearing on the right side ofthe mirror 130 corresponds to the light reflected off of the left sideof the interior surface of the object 110. This is true for all anglesall the way around the mirror 130. Note that the rim 410 is the same rim430 in the image 400. However, the rim 410 is spread out by the mirror130 making it appear larger and, again, the rim 410 in the image is fromthe mirror and corresponds to an opposite side of the soda can.

In accordance with an embodiment of the present invention, there is anoverlap region of the first part of the image 400 and the second part ofthe image 400. That is, a portion of the interior surface of the sodacan appears twice in the image as does the rim (410 and 430). Thisoverlap region corresponds to a transition region on the interiorsurface of the soda can where imaging transitions from the upper portionof the soda can using the mirror 130 to the lower portion of the sodacan using the camera directly. It is desirable to have an overlap regionto ensure that the entire interior surface of the soda can is imagedwithout any gaps between the first part of the image (which is from themirror) and the second part of the image.

Also, it is important to remember that the image 400 is captured as atrue single image and is not a composite of two or more captured images.That is, the mirror and the lower portion of the interior surface of thesoda can is within the field-of-view 145 of the camera 140 such thatonly a single image needs to be captured to have an image of the entireinterior surface of the soda can as well as the rim. In accordance withan embodiment of the present invention, the single camera 140 is a highresolution, high speed digital camera that provides digital imagescomprising 1000 pixels by 1000 pixels (i.e., 1 mega-pixel images).

In FIG. 4, a defect 460 can be seen in the image 400 on the rim (410 and430) of the soda can. Notice that the defect 460 appears twice in theimage. However, on the rim 410 in the image 400, the defect 460 appearson an opposite side compared to the defect 460 on the rim 430 in theimage 400. Again, this is due to the reversal caused by theconfiguration of the mirror 130 with respect to the object to be imaged110. It does not matter that a first part of the image 400 is spread outand reversed by the mirror 130 and that the second part of the image 400appears inside of the first part of the image 400 from the mirror 130.The idea is not to render an image of the soda can as would be seen by ahuman observer looking down on the soda can without the system 100 inplace. Instead, the idea is simply to obtain a single image whichcaptures the entire interior surface of the soda can such that anysignificant defects may be detected.

Consider inspecting a beverage can with a wide-angle lens and a conicalmirror. It is desired to inspect the flange and entire inside of thecan. The flange, sidewall and bottom is imaged directly, while the neckis imaged indirectly through the conical mirror.

Consider a cylindrical can 510 of radius c standing on a table (see FIG.5). Let the unit vectors {circumflex over (x)}ŷ{circumflex over (z)}represent a Cartesian coordinate system where {circumflex over (z)} 520coincides with the can axis and points up, and the origin 530 iscoplanar with the top end of the can. Consider a funnel-shaped (conical)mirror 540 located above the can with the inside of the funnelreflective and facing up, and the cone axis along {circumflex over (z)}.The bottom of the mirror has radius a and is a distance l above the topof the can, and the top of the mirror has radius b and is a distance l+habove the top of the can. Finally, consider a pinhole camera 550 withits optical axis along z looking down into the mirror, with the pinholea distance d above the top of the can and CCD surface 560 a distance f(the lens focal length) above the pinhole.

Because of the cylindrical symmetry of the can-mirror-camera system 500and the assumption of pinhole optics, calculations can be restricted tothe {circumflex over (x)}{circumflex over (z)} plane. Consider a lightray 570 which emerges from a point 580

r _(c) =−c{circumflex over (x)}+z _(c) {circumflex over (z)}  (1)

on the inside surface of the can, then strikes the mirror surface at 590

r _(m) =x _(m) {circumflex over (x)}+z _(m) {circumflex over (z)}  (2)

and is reflected through the camera pinhole onto the image surface at595

r _(i) =x _(i) {circumflex over (x)}+(d+J){circumflex over (z)}.  (3)

Note that both z_(c) and x_(i) are negative, while x_(m) and z_(m) arepositive. It will prove convenient to replace z_(c) and x_(i) withpositive dimensionless parameters

α≡−z _(c) /c

β≡−x _(i) /f  (4)

The goal is to calculate β as a function of a for given a, b, c, d, f hand l The conical shape of the mirror imposes the constraint

$\begin{matrix}{{z_{m} = { + {\gamma \left( {x_{m} - a} \right)}}}{or}} & (5) \\{{x_{m} = {a + {\gamma^{- 1}\left( {z_{m} - } \right)}}},{where}} & (6) \\{{\gamma \equiv \frac{h}{b - a}} = {\tan \; \theta}} & (7)\end{matrix}$

and θ is the angle 596 between the mirror surface and {circumflex over(x)}. The fact that the ray must pass through the pinhole imposes theconstraint

r _(m) +s(r _(i) −r _(m))=d{circumflex over (z)}  (8)

where s is a real parameter. Substituting r_(m) and r_(i) from equations(2) and (3) into (8) and solving yields

$\begin{matrix}{{s = \frac{x_{m}}{x_{m} + {f\; \beta}}}{and}} & (9) \\{\beta = {\frac{x_{m}}{d - z_{m}}.}} & (10)\end{matrix}$

Combining equations (6) and (10) gives

$\begin{matrix}{{\beta = \frac{{\gamma \; a} + \left( {z_{m} - } \right)}{\gamma \left( {d - z_{m}} \right)}}{or}} & (11) \\{z_{m} = {\frac{ - {\gamma \; a} + {\gamma \; d\; \beta}}{1 + {\gamma \; \beta}}.}} & (12)\end{matrix}$

A final constraint is that the angle of incidence must equal the angleof reflection at the mirror. This constraint may be written as

(r _(cm) /|r _(cm)|).t _(m)=(r _(mi) /|r _(mi)|).t _(m),  (13)

where

r _(cm) ≡r _(m) −r _(c)

r _(mi) ≡r _(i) −r _(m)  (14)

and

t _(m) ≡dr _(m) /dx _(m),  (15)

is tangent to the mirror surface at r_(m). Substituting r_(m) fromequation (2) into (15) and using (5) gives

$\quad\begin{matrix}\begin{matrix}{t_{m} = {\hat{x} + {\frac{z_{m}}{x_{m}}\hat{z}}}} \\{= {\hat{x} + {\gamma {\hat{z}.}}}}\end{matrix} & (16)\end{matrix}$

Equation (13) yields multiple solutions for β, but only one inpotentially positive and, thus, of physical interest:

$\begin{matrix}{\beta = {\frac{{c\left( {1 - \gamma^{2}} \right)} + {2{\gamma \left( { - {\gamma \; a}} \right)}} + {2\gamma \; c\; \alpha}}{{2} - {2{\gamma \left( {a + c} \right)}} - {d\left( {1 + \gamma^{2}} \right)} + {{c\left( {1 - \gamma^{2}} \right)}\alpha}}.}} & (17)\end{matrix}$

Solving this equation for a yields

$\begin{matrix}{\alpha = {\frac{{c\left( {1 - \gamma^{2}} \right)} + {2{\gamma \left( { - {\gamma \; a}} \right)}} - {\left( {{2} - {2{\gamma \left( {a + c} \right)}} - {d\left( {1 + \gamma^{2}} \right)}} \right)\beta}}{{{- 2}\gamma \; c} + {{c\left( {1 - \gamma^{2}} \right)}\beta}}.}} & (18)\end{matrix}$

Suppose the can radius c is given and we have selected a candidatecamera-lens combination with lens focal length f and maximum imageradius β_(max) on the CCD. (Recall that image radii are expressed asfractions of f.)

The direct image of the can falls on the CCD within the radius

$\begin{matrix}{{\beta \; o} = {\frac{c}{d}.}} & (19)\end{matrix}$

The indirect (neck) image covers an annulus with inner radius

$\begin{matrix}{\beta_{1} = \frac{a}{d - }} & (20)\end{matrix}$

and outer radius β₂, where β₁ and β₂ correspond to the lowest andhighest portions of the neck imaged. The indirect image must not occludethe direct image so

β₁≧β₀.  (21)

To utilize the CCD efficiently, it is desired that

β₁≅β₀.  (22)

In all cases of interest, the bottom of the mirror is much closer to thecan than is the pinhole (l<<d), so the condition

a=c  (23)

is a practical way to enforce (22) while still leaving a gap between β₀and β₁ to accommodate mechanical tolerances and slight mis-centering ofthe can. It is desirable to image the neck all the way to the top of thecan (α=0), so from equation (17) is obtained

$\begin{matrix}{\beta_{2} = \frac{{c\left( {1 - \gamma^{2}} \right)} + {2{\gamma \left( { - {\gamma \; a}} \right)}}}{{2} - {2{\gamma \left( {a + c} \right)}} - {d\left( {1 + \gamma^{2}} \right)}}} & (24)\end{matrix}$

which implies

$\begin{matrix}{{{\gamma \pm} = \frac{A \pm \sqrt{A^{2} + {BC}}}{B}}{where}} & (25) \\{{A \equiv { + {\left( {a + c} \right)\beta_{2}}}}{B \equiv {{2a} + c - {d\; \beta_{2}}}}{C \equiv {c + {\left( {d - {2}} \right){\beta_{2}.}}}}} & (26)\end{matrix}$

The values of β₀ and β₂ dictate how the available CCD surface isallocated to direct and indirect imaging, and they satisfy

0<β₀<β₂<β_(max).  (27)

It will prove convenient to define

ρ₀≡β₀/β_(max)

ρ₂≡β₂/β_(max),  (28)

where

0<ρ₀<ρ₂<1.  (29)

The value of l is at the disposal of the designer, so long as theassumption l<<d made in conjunction with equation (23) is satisfied. Inpractice l should be just large enough to avoid mechanical jams and toallow illuminating the inside of the can from below the mirror.

The design process for a conical mirror is now desired. Values of c, fand β_(max) are given and the designer selects values of ρ₀, ρ₂ and l.Then β₀ and β₂ are determined from equations (28), d and a determinedfrom equations (19) and (23), and the physically appropriate (positive)solution for γ is determined from equation (25).

Consider inspecting a beverage can of radius c=33 mm using a camera-lenscombination with f=6.5 mm and β_(max)=0.46 (i.e., the Jenoptik P lensand a megapixel camera). Devote 50% of the image width to the directimage (ρ_(o)=0.5) and another 40% to the indirect image (ρ₂=0.9). Letthe bottom of the mirror be l=15 mm above the can. These equations (28)give

β₀=0.230

β₂=0.414,  (30)

equations (19) and (23) give

d=143 mm

a=33 mm,  (31)

and equation (25) gives

γ=2.85.  (32)

This value of γ corresponds to a cone angle (measured from thehorizontal) of Θ=71°.

The location of the top of the mirror can be calculated from equation(12) with β=β₂, which gives

l+h=41 mm  (33)

and implies a mirror height of

h=26 mm.  (34)

This is actually the minimum permissible mirror height. In practice, oneshould make the mirror somewhat larger, to accommodate mechanicaltolerances and slight mis-centering of the can.

It is of interest to calculate how far down the neck the mirror sees.This location corresponds to (see equation (20))

β₁=0.257.  (35)

Substituting this value into equation (18) gives

α=1.05.  (36)

Then from (4) we obtain

|z_(c)|=35 mm  (37)

which is the maximum distance down the neck imaged by the mirror.

FIG. 6 is a plot of equation (17). It shows the radial location on theCCD (β) corresponding to a given distance down the can neck (α). Recallthat α and β are expressed in terms of c and f respectively. Note thatthe mapping from α to β is nearly linear.

In summary, a system and method is disclosed for imaging the entireinterior surface of a substantially cylindrical object, such as abeverage can, by capturing a single image with a single camera. Theimage is subsequently analyzed for defects such as dents and puckers.Such a system may be installed as part of a manufacturing line to detectdefects of objects passing along the line such that the defectiveobjects may be rejected.

While the invention has been described with reference to certainembodiments, it will be understood by those skilled in the art thatvarious changes may be made and equivalents may be substituted withoutdeparting from the scope of the invention. In addition, manymodifications may be made to adapt a particular situation or material tothe teachings of the invention without departing from its scope.Therefore, it is intended that the invention not be limited to theparticular embodiment disclosed, but that the invention will include allembodiments falling within the scope of the appended claims.

1. An apparatus for illuminating at least a portion of an interior of atleast one substantially cylindrical object, said apparatus comprising:an LED holder forming a substantially cylindrical surface; and aplurality of LEDs positioned around and held in place by said LED holderforming a substantially cylindrical arrangement of said plurality ofLEDs such that an axis of illumination of each LED of said plurality ofLEDs points substantially into an interior cylindrical volumecircumscribed by said LED holder.
 2. The apparatus of claim 1 wherein ahorizontal directional component of illumination of each LED of saidplurality of LEDs, in any imaginary horizontal plane crossing throughsaid substantially cylindrical surface, is pointed such that saidhorizontal directional component of illumination does not intersect animaginary vertical central axis of said interior cylindrical volume. 3.The apparatus of claim 2 wherein said horizontal directional componentof illumination of said each LED is pointed at a same predeterminedhorizontal angle with respect to a horizontal directional component ofillumination of an adjacent LED in a same horizontally oriented row ofsaid substantially cylindrical arrangement of said plurality of LEDs. 4.The apparatus of claim 1 wherein an elevational directional component ofillumination of each LED in a first horizontally oriented row of saidsubstantially cylindrical arrangement of said plurality of LEDs ispointed downward at a first elevational angle with respect tohorizontal.
 5. The apparatus of claim 1 wherein an elevationaldirectional component of illumination of each LED in a secondhorizontally oriented row of said substantially cylindrical arrangementof said plurality of LEDs is pointed downward at a second elevationalangle with respect to horizontal.
 6. The apparatus of claim 1 wherein anelevational directional component of illumination of each LED in a thirdhorizontally oriented row of said substantially cylindrical arrangementof said plurality of LEDs is pointed downward at a third elevationalangle with respect to horizontal.
 7. The apparatus of claim 1 wherein anelevational directional component of illumination of each LED in afourth horizontally oriented row of said substantially cylindricalarrangement of said plurality of LEDs is pointed downward at a fourthelevational angle with respect to horizontal.
 8. The apparatus of claim1 further comprising a flexible printed circuit board wrapped aroundsaid substantially cylindrical surface of said LED holder.
 9. Theapparatus of claim 1 wherein said LED holder includes at least one lipprotruding away from said substantially cylindrical surface to protectsaid plurality of LEDs from being damaged.
 10. The apparatus of claim 1wherein said LED holder comprises a non-conductive, machineable,environmentally stable material.
 11. The apparatus of claim 1 whereinsaid LED holder includes holes to accept conductive leads of saidplurality of LEDs.
 12. The apparatus of claim 1 wherein saidsubstantially cylindrical arrangement of said plurality of LEDscomprises four horizontally stacked, circular rows of LEDs.